"if you think childlike, you'll stay young. If you keep your energy going, and do everything with a little flair, you're gunna stay young. But most people do things without energy, and they atrophy their mind as well as their body. you have to think young, you have to laugh a lot, and you have to have good feelings for everyone in the world, because if you don't, it's going to come inside, your own poison, and it's over" Jerry Lewis
"I don’t believe
in the irreversibility of situations" Deleuze

Note on Citations

The numerical citations refer to page number. The source's text-space (including footnote region) is divided into four equal portions, a, b, c, d. If the citation is found in one such section, then for example it would be cited p.15c. If the cited text lies at a boundary, then it would be for example p.16cd. If it spans from one section to another, it is rendered either for example p.15a.d or p.15a-d. If it goes from a 'd' section and/or arrives at an 'a' section, the letters are omitted: p.15-16.

[The following is summary, up to the end where I reproduce this section in full. My commentary is in brackets.]

David Hume

A Treatise of Human Nature

Book I: Of the Understanding

Part I: Of Ideas, their Origin, Composition, Connexion, Abstraction, etc.

Section VII: "Of Abstract Ideas"

§45

Regarding abstract or general ideas, Hume asks if the mind conceives them as general or particular. Berkeley argues that all general ideas are particular ideas affixed to some particular term. This "gives them a more extensive signification." It also allows us to more easily recall related individuals. Hume will proceed to defend Berkeley's argument.

§46

Objects are given to us in shades or degrees of quantities and qualities. But when we form general ideas of objects, we abstract from these degrees of quality and quantity. And by so slightly altering its extension, duration, and other properties, the object ceases to be of a particular species.

A general idea represents all things of its kind. So the abstract idea of 'man' represents all men of every size and quality. But, we know that the idea cannot represent every one of these possibilities all once. And we know that it also must represent some particular; for, we cannot conceive an idea without also having some particular in our mind. Hence our philosophical dilemma. The first option, that one idea represents all possible instances all at once, is rejected because it produces an infinite regress, [for there is an infinity of possibilities, so no idea could ever represent them all at once.] Thus many conclude instead that general ideas cannot represent particulars.

Hume will argue the contrary.

it is utterly impossible to conceive any quantity or quality, without forming a precise notion of its degrees.

Hume acknowledges that the mind is not infinite. However, he will argue nonetheless that we can form an imperfect notion of all the possible qualitative and quantitative degrees of the object.

§47

Hume will prove the following proposition through three arguments:

THE MIND CANNOT FORM ANY NOTION OF QUANTITY OR QUALITY WITHOUT FORMING A PRECISE NOTION OF DEGREES OF EACH.

Argument 1:

If objects

a) differ, they may be

b) distinguished. And if objects are distinguishable, they may be

c) separated in the thought and imagination.

Likewise, objects which are

a) separable are

b) distinguishable. And distinguishable objects are

c) different.

Now Hume must establish that in all cases of abstraction, the abstracted notion is different from its varying instantiations.

He notes that we cannot conceive of a line without also conceiving that line having some length.

the precise length of a line is not different nor distinguishable from the line itself, nor the precise degree of any quality from the quality.

Therefore, ideas are not distinct from the quantities and qualities of their respective objects.

However, we may generalize ideas in this way: when conceiving of a line in general, we conceive of a line with its precise degrees of quantity and quality, but we think that we may just as well have conceived a line of any other precise degree of quantity and quality. So generality, for Hume, is a matter of the scope of the arbitrariness of precise ideas.

§48

Argument 2:

Objects appear to our senses. This requires that an impression enters our minds. To do so, the object must be determined in both its degrees of quantity and quality.

True, some likewise argue that is necessary for objects to be determined in terms of their degrees of quantity and quality. Yet, they also argue that when impressions are faint, it is not on account of some inadequacy of our mind's ability to receive impressions. They think that instead, the objects themselves have no particular degree or proportion, and hence our minds are unable to assign any degrees of quantity and quality to them. [So in other words, some hold that our abstract ideas are really faint ones which do not have precise determinations.]

But, Hume says, to say that an object does not have degrees of qualities and quantities is a contradiction of terms. For, every object has properties.

Ideas are copies and representations of impressions. So what is true for the one is true for the other. The only way that impressions and ideas are different is in their degree of strength and vivacity. An idea is a weak impression. But all strong impressions have determinate degrees of quantity and quality. So it is also true of their copies or representations, that is, their ideas. No matter how "faint," all ideas must also have determinate quantities and qualities.

§49

Argument 3;

Some philosophers hold that everything in nature is individual. So, there are no triangles in reality without precise proportions between their sides and angles. And because it is absurd for there to be indeterminate triangles in fact and reality, it is also impossible that we may have an idea of a triangle without such precise determinations. For, we cannot form ideas that are absurd and impossible.

In the case of the triangle, we form an idea of an object. To think merely of a triangle in general is no different of an act of forming an idea. So say we form an idea of an object, like a triangle, that possesses properties of quantity and quality. We cannot form this idea without also forming an idea of the precise degrees of the triangle's quantities and qualities.

Hence we can only form ideas– no matter which ones– that are bound to certain particulars. In this way, all abstract ideas are individual. However, abstract ideas may become general if we apply the particular image in our mind to wide variety of particular cases, as if it were a universal.

§50

So to universalize an idea, we broaden its application beyond its "nature." We do so by collecting all the object's possible degrees of quantity and quality in just enough of an imperfect manner that the idea may better serve our given purposes for it.

When several objects resemble each other, we apply a common name to all of them, despite whatever differences exist between their degrees of quantity and quality, and despite whatever other differences they share.

We then become accustomed to considering the similar objects under a common name. So someone else's use of that term revives in our mind the idea of any one of these objects. The imagination then conceives this one instance of the commonly named object in all its particular properties and proportions.

But when we use the common word, it does not evoke every other related notion that applies to it. Rather, the word only revives our customary way of using it.These other implicitly-possible applications of the word are present to the mind as potencies:

They are not really and in fact present to the mind, but only in power.

So we do not consider each potential application individually. Rather, we

keep ourselves in a readiness to survey any of them, as we may be prompted by a present design or necessity.

Because we cannot take into account every possible application, we only consider them in part. But we encounter but few problems in doing so.

§51

When we hear the word triangle, perhaps the individual idea that comes to our mind is an equilateral triangle. Then we might conclude that the three angles of a triangle are equal to each other. Just then, other such individual triangles as scalene and isosceles "immediately crowd in upon us, and make us perceive the falsehood of this proposition." For Hume, this is one of the "most extraordinary circumstances in the present affair." When we generalize an individual idea, we are not making it less determinate. Rather, first we think of a specific idea. This activates our custom of searching for other ideas that do not agree with that particular one, but which also we habitually apply to that common term. This way, even though we can only think determinate ideas, we still may generalize their application.

§52

We have the custom of attaching one idea to different words, so that it may be applied in different cases of reasoning. Hence, the idea of an equilateral triangle whose sides are one inch may serve us when talking about triangles, or more broadly when we are discussing regular figures. What matters is that when the idea serves in discussing triangles, we take a square as an exception. But when we are discussing regular figures, and we think a triangle, in that case it is appropriate for the idea of a square to suggest itself as an additional application for the term "regular figure." The reason the square enters our mind is because we are accustomed to thinking of the square also when discussing regular figures.

So when we think such a particular idea, we also consider its range of application. For, the individual idea excites in our mind the habits appropriate for the given generalization of the ideas application.

So perhaps we are thinking of an equilateral triangle when considering regular figures. Then someone speaks of a rectangle as such a regular figure. Immediately our minds will object. For, our minds will not be able to produce any specific idea of a square which we are accustomed to also call a "regular figure." Thus individual ideas "keep the mind in a readiness to observe, that no conclusion be formed contrary to any ideas, which are usually comprized under them."

§53

We think the idea of a circle when using the word "figure," and we are implicitly on guard for related ideas that do not apply to this term. In this way, we may both think a specific idea but refer to a whole class of similar ideas.

Ideally, we would only need to think one idea for such a generalization. But this optimum case only occurs after we have perfected our habits of applying terms to particular ideas while excluding those which we do not habitually apply to that term.

Our abilities to generalize the application of specific ideas is perfected through practice. But before our habits become perfect, we perhaps will need to imagine more than one idea to make a generalization. So early on we will need to consider a couple ideas that apply to the common term. However, we know for certain

1) that we form the ideas of individuals,

2) that we almost never exhaust all possible individuals, and

3) that habit will still recall in other situations those individual ideas which we do not consider in a particular instance.

The equilateral triangle was a specific idea. As well, it implicitly represented all other ideas that apply to the term "regular figure." In this way Hume accounts for the paradox:

that some ideas are particular in their nature, but general in their representation.

The idea of the equilateral triangle becomes generalized when we attach it to the general term "regular figure." What makes this term general is

1) we are accustomed to applying a variety of specific ideas to it, and

2) we easily recall these other ideas when using this general term.

§54

Hume will now describe our mind's operation of producing the proper idea upon hearing some word or sound. But we are incapable of giving the ultimate causes of our mental actions. So we instead will analogize from particular experiences.

Ways our minds produce the ideas proper to their respective words:

§55

1) Production from more adequate ideas:

When we say "a thousand" or any other such large number, we are not able also to conceive an adequate idea of what "a thousand" is. However, our minds do have the power to produce the idea "a thousand." It does so by means of our adequate idea of the decimals. Under this idea we comprehend a variety of numbers, including one thousand.

This instance involves our habits of finding specific ideas that we customarily apply to certain ideas. So it is much like how we treat universal ideas.

The idea of "a thousand" is not a complete concrete idea, so it is somewhat imperfect. Nonetheless, our power of reasoning is not imperfect. For, it is perfectly capable of producing an adequate idea from inadequate ones in this way.

§56

2) Total recall from a single index word:

Actors memorize large passages of dialogue. But sometimes they forget their lines while performing. Often all they need is someone offstage to say the first word or phrase, and then they immediately recall the entire passage. In these cases, habits of associating the dialogue with its component words strengthen its potential for recall. All that is needed to revive the whole passage is merely the suggestion of one word or expression at its beginning.

§57

3) Implicit evocations of our habitual applications:

Consider the relatively simple ideas for the terms 'war,' 'the weaker,' 'recourse,' and 'conquest.' When we hear the term 'war,' some particular idea of a specific war comes to mind. However in other instances perhaps we considered some different determine idea of a war. We gradually develop the habit of evoking this collection of particulars. And as we develop this habit, we also develop the ability to know what other specific related ideas we do not normally evoke when hearing the term 'war.' So we know what individual ideas correspond to the word 'war,' and which ones do not, based on our habits of making these evocations in our minds.

So each one of these ideas has a range of applicability [i.e., an extension]. We can combine these simple ideas to create a complex idea, for example:

"in war, the weaker have always recourse to negotiation."

It is possible that when considering the complex idea as a whole, we are not thereby considering the extension for each constituent simple idea. However, our customs for associating these particular words to simple ideas is brought to life even when we consider the complex idea as a whole. Therefore, we are also implicitly aware of the ideas which do not apply to each term. In this case, the ideas which apply to the terms "weaker" and "negotiation" do not relate contrarily to each other.

However, consider this other complex idea:

"the weaker in war have always recourse to conquest."

In this case as well, we do not evoke in our minds the specific ideas for each term. However, still our habits of applying specific ideas to each term are evoked. What we find then is a conflict between our habits. For, our habit of applying ideas to the word 'weaker' and to the word 'conquest' will butt into each other. One effort will counter-act the other, because they will tend to produce specific ideas with relations of contrariety. [In a Deleuzean sense, our contrary habits here are producing intensities, because each habit is a force acting against the other one; each is tending a different way, which opens up tendings tending in to new dimensions of thought. These new dimensional directions are virtualities, or intensities. In such moments, thought begins to 'stutter.']

§58

4) Habitual recollections strengthen with further repetitions:

The more our minds collect resembling individuals and place them under a general term, the more easily our minds will associate them. Hence the more readily will the imagination suggest particular ideas when the general term is considered.

Nothing is more admirable, than the readiness, with which the imagination suggests its ideas, and presents them at the very instant, in which they become necessary or useful. The fancy runs from one end of the universe to the other in collecting those ideas, which belong to any subject.

It is as though all ideas were pre-classified and ready for us to pick-out any one of them for our given purposes.

However, there is not some Platonic realm containing all ideas ready-made and pre-classified. Rather, the only ideas available to us are those that are "collected by a kind of magical faculty in the soul." It is beyond our capacities to understand this magical faculty that organizes our ideas, even though we do know that this faculty is most perfect in geniuses.

§59

Hume hopes that his above argumentation convinces us that there are no general ideas. Hume accounts for abstract generalizations as being the breath of the collection of ideas applicable to a common word. He does not think that there are any ideas that are unspecific enough that more precise ones may fall under them.

We have a finite amount of precise ideas, and they may be grouped according to our habits of associating them. But even though their number is finite, there still remains the possibility that an infinity of other ideas may be grasped and applied to some common term.

We must certainly seek some new system on this head, and there plainly is none beside what I have proposed. If ideas be particular in their nature, and at the same time finite in their number, it is only by custom they can become general in their representation, and contain an infinite number of other ideas under them.

§60

Hume then addresses a difficulty his contemporaries struggled-with. We have an object, and it has a form. The two are distinct, and yet inseparable. Also, we have a moving body, and we have its motion. Again, both are distinct but inseparable. Hume firstly notes that if ideas are different from each other, then they are separable from each other.

a) If these things are truly different from one another, then their ideas should be separable as well, but

b) if they are not different, then their ideas should be neither separable nor distinguishable.

Here we have a "distinction of reason," but strangely it seems to imply neither a difference nor a separation

§61

When we see a white globe of marble, we receive its whiteness as it is given in this spherical form. We do not have separate impressions of white and sphere. So we are unable to distinguish color from form in that impression. Hence the mind would also not naturally consider an object as separate from its form.

However, after we are shown the globe of white marble, we are then shown:

1) a globe of black marble, and

2) a cube of white marble.

Then, we compare them to find two resemblances:

a) color: the white globe and the white cube are both white

b) form: the white globe and the black globe are both spheres

Then, we begin to form a habit of calling to mind either the white cube or the white sphere when using the term "white." Likewise, we begin here in this moment to develop the habit of calling to mind either the black globe or the white globe when considering the term "sphere." On account of their resemblance, we extend our application of a common term to either idea [that is to say, we incorporate both resembling ideas into the extension of ideas which we habitually call to mind when considering their proper term.]

So we see a white globe. We say, "white globe." We accomplished this not by distinguishing its whiteness from its sphericity, for they reside together and are inseparable. Rather, this one object evokes two habits of application for similar ideas. So when we see the white globe, we also might tend towards imagining the white cube, or towards any other idea of some white thing. At the same time, our habits are tending towards other evocations, for we also might imagine the black sphere, or any other ideas of spherical objects.

So we do not separate the whiteness from the sphericity. However, our habits diverge into separate tendencies of associating resembling objects. This divergence does not mean that the whiteness and the sphericity of the white globe are really different. Rather, it means that our associations tend in more than one way. Such a distinction is not a real distinction, but what Hume calls a 'distinction of reason.'

After a little more practice of this kind, we begin to distinguish the figure from the colour by a distinction of reason; that is, we consider the figure and colour together, since they are in effect the same and undistinguishable; but still view them in different aspects, according to the resemblances, of which they are susceptible.

When we want only to discuss the whiteness of the white marble globe, we cannot conceive it separately from its sphericity. What we do instead is emphasize its resemblance to the white cube or to any other white thing whatever. These selective emphases on particular habits of association is a sort of reflective thinking, but it is one that is insensible to us. For, we become so accustomed to doing it that we cease noticing the operation.

A very material question has been started concerning ABSTRACT or GENERAL ideas, WHETHER THEY BE GENERAL OR PARTICULAR IN THE MIND’S CONCEPTION OF THEM. A great philosopher [Dr. Berkeley.] has disputed the received opinion in this particular, and has asserted, that all general ideas are nothing but particular ones, annexed to a certain term, which gives them a more extensive signification, and makes them recall upon occasion other individuals, which are similar to them. As I look upon this to be one of the greatest and most valuable discoveries that has been made of late years in the republic of letters, I shag here endeavour to confirm it by some arguments, which I hope will put it beyond all doubt and controversy.

It is evident, that in forming most of our general ideas, if not all of them, we abstract from every particular degree of quantity and quality, and that an object ceases not to be of any particular species on account of every small alteration in its extension, duration and other properties. It may therefore be thought, that here is a plain dilemma, that decides concerning the nature of those abstract ideas, which have afforded so much speculation to philosophers. The abstract idea of a man represents men of all sizes and all qualities; which it is concluded it cannot do, but either by representing at once all possible sizes and all possible qualities, or by, representing no particular one at all. Now it having been esteemed absurd to defend the former proposition, as implying an infinite capacity in the mind, it has been commonly inferred in favour of the letter: and our abstract ideas have been supposed to represent no particular degree either of quantity or quality. But that this inference is erroneous, I shall endeavour to make appear, first, by proving, that it is utterly impossible to conceive any quantity or quality, without forming a precise notion of its degrees: And secondly by showing, that though the capacity of the mind be not infinite, yet we can at once form a notion of all possible degrees of quantity and quality, in such a manner at least, as, however imperfect, may serve all the purposes of reflection and conversation.

To begin with the first proposition, THAT THE MIND CANNOT FORM ANY NOTION OF QUANTITY OR QUALITY WITHOUT FORMING A PRECISE NOTION OF DEGREES OF EACH; we may prove this by the three following arguments. First, We have observed, that whatever objects are different are distinguishable, and that whatever objects are distinguishable are separable by the thought and imagination. And we may here add, that these propositions are equally true in the inverse, and that whatever objects are separable are also distinguishable, and that whatever objects are distinguishable, are also different. For how is it possible we can separate what is not distinguishable, or distinguish what is not different? In order therefore to know, whether abstraction implies a separation, we need only consider it in this view, and examine, whether all the circumstances, which we abstract from in our general ideas, be such as are distinguishable and different from those, which we retain as essential parts of them. But it is evident at first sight, that the precise length of a line is not different nor distinguishable from the line itself. nor the precise degree of any quality from the quality. These ideas, therefore, admit no more of separation than they do of distinction and difference. They are consequently conjoined with each other in the conception; and the general idea of a. line, notwithstanding all our abstractions and refinements, has in its appearance in the mind a precise degree of quantity and quality; however it may be made to represent others, which have different degrees of both. Secondly, it is contest, that no object can appear to the senses; or in other words, that no impression can become present to the mind, without being determined in its degrees both of quantity and quality. The confusion, in which impressions are sometimes involved, proceeds only from their faintness and unsteadiness, not from any capacity in the mind to receive any impression, which in its real existence has no particular degree nor proportion. That is a contradiction in terms; and even implies the flattest of all contradictions, viz. that it is possible for the same thing both to be and not to be.

Now since all ideas are derived from impressions, and are nothing but copies and representations of them, whatever is true of the one must be acknowledged concerning the other. Impressions and ideas differ only in their strength and vivacity. The foregoing conclusion is not founded on any particular degree of vivacity. It cannot therefore be affected by any variation in that particular. An idea is a weaker impression; and as a strong impression must necessarily have a determinate quantity and quality, the case must be the same with its copy or representative.

Thirdly, it is a principle generally received in philosophy that everything in nature is individual, and that it is utterly absurd to suppose a triangle really existent, which has no precise proportion of sides and angles. If this therefore be absurd in fact and reality, it must also be absurd in idea; since nothing of which we can form a clear and distinct idea is absurd and impossible. But to form the idea of an object, and to form an idea simply, is the same thing; the reference of the idea to an object being an extraneous denomination, of which in itself it bears no mark or character. Now as it is impossible to form an idea of an object, that is possest of quantity and quality, and yet is possest of no precise degree of either; it follows that there is an equal impossibility of forming an idea, that is not limited and confined in both these particulars. Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a particular object, though the application of it in our reasoning be the same, as if it were universal.

This application of ideas beyond their nature proceeds from our collecting all their possible degrees of quantity and quality in such an imperfect manner as may serve the purposes of life, which is the second proposition I proposed to explain. When we have found a resemblance2 among several objects, that often occur to us, we apply the same name to all of them, whatever differences we may observe in the degrees of their quantity and quality, and whatever other differences may appear among them. After we have acquired a custom of this kind, the hearing of that name revives the idea of one of these objects, and makes the imagination conceive it with all its particular circumstances and proportions. But as the same word is supposed to have been frequently applied to other individuals, that are different in many respects from that idea, which is immediately present to the mind; the word not being able to revive the idea of all these individuals, but only touches the soul, if I may be allowed so to speak, and revives that custom, which we have acquired by surveying them. They are not really and in fact present to the mind, but only in power; nor do we draw them all out distinctly in the imagination, but keep ourselves in a readiness to survey any of them, as we may be prompted by a present design or necessity. The word raises up an individual idea, along with a certain custom; and that custom produces any other individual one, for which we may have occasion. But as the production of all the ideas, to which the name may be applied, is in most eases impossible, we abridge that work by a more partial consideration, and find but few inconveniences to arise in our reasoning from that abridgment.

2 It is evident, that even different simple ideas may have a similarity or resemblance to each other; nor is it necessary, that the point or circumstance of resemblance shoud be distinct or separable from that in which they differ. BLUE and GREEN are different simple ideas, but are more resembling than BLUE and SCARLET; tho their perfect simplicity excludes all possibility of separation or distinction. It is the same case with particular sounds, and tastes and smells. These admit of infinite resemblances upon the general appearance and comparison, without having any common circumstance the same. And of this we may be certain, even from the very abstract terms SIMPLE IDEA. They comprehend all simple ideas under them. These resemble each other in their simplicity. And yet from their very nature, which excludes all composition, this circumstance, In which they resemble, Is not distinguishable nor separable from the rest. It is the same case with all the degrees In any quality. They are all resembling and yet the quality, In any individual, Is not distinct from the degree.

For this is one of the most extraordinary circumstances in the present affair, that after the mind has produced an individual idea, upon which we reason, the attendant custom, revived by the general or abstract term, readily suggests any other individual, if by chance we form any reasoning, that agrees not with it. Thus should we mention the word triangle, and form the idea of a particular equilateral one to correspond to it, and should we afterwards assert, that the three angles of a triangle are equal to each other, the other individuals of a scalenum and isosceles, which we overlooked at first, immediately crowd in upon us, and make us perceive the falshood of this proposition, though it be true with relation to that idea, which we had formed. If the mind suggests not always these ideas upon occasion, it proceeds from some imperfection in its faculties; and such a one as is often the source of false reasoning and sophistry. But this is principally the case with those ideas which are abstruse and compounded. On other occasions the custom is more entire, and it is seldom we run into such errors.

Nay so entire is the custom, that the very same idea may be annext to several different words, and may be employed in different reasonings, without any danger of mistake. Thus the idea of an equilateral triangle of an inch perpendicular may serve us in talking of a figure, of a rectilinear figure, of a regular figure, of a triangle, and of an equilateral triangle. AR these terms, therefore, are in this case attended with the same idea; but as they are wont to be applied in a greater or lesser compass, they excite their particular habits, and thereby keep the mind in a readiness to observe, that no conclusion be formed contrary to any ideas, which are usually comprized under them.

Before those habits have become entirely perfect, perhaps the mind may not be content with forming the idea of only one individual, but may run over several, in order to make itself comprehend its own meaning, and the compass of that collection, which it intends to express by the general term. That we may fix the meaning of the word, figure, we may revolve in our mind the ideas of circles, squares, parallelograms, triangles of different sizes and proportions, and may not rest on one image or idea. However this may be, it is certain that we form the idea of individuals, whenever we use any general term; that we seldom or never can exhaust these individuals; and that those, which remain, are only represented by means of that habit, by which we recall them, whenever any present occasion requires it. This then is the nature of our abstract ideas and general terms; and it is after this manner we account for the foregoing paradox, THAT SOME IDEAS ARE PARTICULAR IN THEIR NATURE, BUT GENERAL IN THEIR REPRESENTATION. A particular idea becomes general by being annexed to a general term; that is, to a term, which from a customary conjunction has a relation to many other particular ideas, and readily recalls them in the imagination.

The only difficulty, that can remain on this subject, must be with regard to that custom, which so readily recalls every particular idea, for which we may have occasion, and is excited by any word or sound, to which we commonly annex it. The most proper method, in my opinion, of giving a satisfactory explication of this act of the mind, is by producing other instances, which are analogous to it, and other principles, which facilitate its operation. To explain the ultimate causes of our mental actions is impossible. It is sufficient, if we can give any satisfactory account of them from experience and analogy. First then I observe, that when we mention any great number, such as a thousand, the mind has generally no adequate idea of it, but only a power of producing such an idea, by its adequate idea of the decimals, under which the number is comprehended. This imperfection, however, in our ideas, is never felt in our reasonings; which seems to be an instance parallel to the present one of universal ideas.

Secondly, we have several instances of habits, which may be revived by one single word; as when a person, who has by rote any periods of a discourse, or any number of verses, will be put in remembrance of the whole, which he is at a loss to recollect, by that single word or expression, with which they begin.

Thirdly, I believe every one, who examines the situation of his mind in reasoning will agree with me, that we do not annex distinct and compleat ideas to every term we make use of, and that in talking of government, church, negotiation, conquest, we seldom spread out in our minds all the simple ideas, of which these complex ones are composed. It is however observable, that notwithstanding this imperfection we may avoid talking nonsense on these subjects, and may perceive any repugnance among the ideas, as well as if we had a fall comprehension of them. Thus if instead of saying, that in war the weaker have always recourse to negotiation, we should say, that they have always recourse to conquest, the custom, which we have acquired of attributing certain relations to ideas, still follows the words, and makes us immediately perceive the absurdity of that proposition; in the same manner as one particular idea may serve us in reasoning concerning other ideas, however different from it in several circumstances.

Fourthly, As the individuals are collected together, said placed under a general term with a view to that resemblance, which they bear to each other, this relation must facilitate their entrance in the imagination, and make them be suggested more readily upon occasion. And indeed if we consider the common progress of the thought, either in reflection or conversation, we shall find great reason to be satisfyed in this particular. Nothing is more admirable, than the readiness, with which the imagination suggests its ideas, and presents them at the very instant, in which they become necessary or useful. The fancy runs from one end of the universe to the other in collecting those ideas, which belong to any subject. One would think the whole intellectual world of ideas was at once subjected to our view, and that we did nothing but pick out such as were most proper for our purpose. There may not, however, be any present, beside those very ideas, that are thus collected by a kind of magical faculty in the soul, which, though it be always most perfect in the greatest geniuses, and is properly what we call a genius, is however inexplicable by the utmost efforts of human understanding.

Perhaps these four reflections may help to remove an difficulties to the hypothesis I have proposed concerning abstract ideas, so contrary to that, which has hitherto prevailed in philosophy, But, to tell the truth I place my chief confidence in what I have already proved concerning the impossibility of general ideas, according to the common method of explaining them. We must certainly seek some new system on this head, and there plainly is none beside what I have proposed. If ideas be particular in their nature, and at the same time finite in their number, it is only by custom they can become general in their representation, and contain an infinite number of other ideas under them.

Before I leave this subject I shall employ the same principles to explain that distinction of reason, which is so much talked of, and is so little understood, in the schools. Of this kind is the distinction betwixt figure and the body figured; motion and the body moved. The difficulty of explaining this distinction arises from the principle above explained, that all ideas, which are different, are separable. For it follows from thence, that if the figure be different from the body, their ideas must be separable as well as distinguishable: if they be not different, their ideas can neither be separable nor distinguishable. What then is meant by a distinction of reason, since it implies neither a difference nor separation.

To remove this difficulty we must have recourse to the foregoing explication of abstract ideas. It is certain that the mind would never have dreamed of distinguishing a figure from the body figured, as being in reality neither distinguishable, nor different, nor separable; did it not observe, that even in this simplicity there might be contained many different resemblances and relations. Thus when a globe of white marble is presented, we receive only the impression of a white colour disposed in a certain form, nor are we able to separate and distinguish the colour from the form. But observing afterwards a globe of black marble and a cube of white, and comparing them with our former object, we find two separate resemblances, in what formerly seemed, and really is, perfectly inseparable. After a little more practice of this kind, we begin to distinguish the figure from the colour by a distinction of reason; that is, we consider the figure and colour together, since they are in effect the same and undistinguishable; but still view them in different aspects, according to the resemblances, of which they are susceptible. When we would consider only the figure of the globe of white marble, we form in reality an idea both of the figure and colour, but tacitly carry our eye to its resemblance with the globe of black marble: And in the same manner, when we would consider its colour only, we turn our view to its resemblance with the cube of white marble. By this means we accompany our ideas with a kind of reflection, of which custom renders us, in a great measure, insensible. A person, who desires us to consider the figure of a globe of white marble without thinking on its colour, desires an impossibility but his meaning is, that we should consider the figure and colour together, but still keep in our eye the resemblance to the globe of black marble, or that to any other globe of whatever colour or substance.